Invertibility of Linear Transformations

• A linear transformation is invertible iff:

$$\begin{array}{r}M\circ L=\text{Id}=L\circ M\\ \\ L^{-1}=M\end{array}$$

• A tf is invertible if we can find another tf that “cancels out” the effect of the first transformation.

• This translates nicely to their associated matrices:

$$[L{]}^{-1}=[M]$$